4x + 3y = 0
2x - y = 0
multiply the bottom equation by 2 on both sides
4x + 3y = 0
4x - 2y = 0
subtract 3y from both sides in the top equation and add 2y to both sides in the bottom equations
4x = -3y
4x = 2y
see how the left side of both equations is 4x? the same? that means the right sides are the same too, so we can do this:
-3y = 2y
-5y = 0
y = 0
2x - y = 0
2x - 0 = 0
2x = 0
x = 0
Answer: x = 0, y = 0